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A257024 Number of squares in the quarter-sum representation of n. 5
1, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 1, 2, 1, 2, 2, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 0, 1, 0, 1, 1, 2, 0, 1, 2, 1, 2, 2, 3, 1, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 1, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Every positive integer is a sum of at most four distinct quarter squares; see A257019.

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..1000

EXAMPLE

Quarter-square representations:

r(5) = 4 + 1, so a(5) = 2;

r(11) = 9 + 2, so a(11) = 1;

r(35) = 30 + 4 + 1, so a(35) = 2.

MATHEMATICA

z = 100; b[n_] := Floor[(n + 1)^2/4]; bb = Table[b[n], {n, 0, 100}];

s[n_] := Table[b[n], {k, b[n + 1] - b[n]}];

h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];

g = h[100]; Take[g, 100]; r[0] = {0};

r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]]

sq = Table[n^2, {n, 0, 1000}]; t = Table[r[n], {n, 0, z}]

u = Table[Length[Intersection[r[n], sq]], {n, 0, 250}]

CROSSREFS

Cf. A002620, A257019, A257020, A257021, A257022.

Sequence in context: A190487 A054528 A025884 * A124433 A287104 A190483

Adjacent sequences:  A257021 A257022 A257023 * A257025 A257026 A257027

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 15 2015

STATUS

approved

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Last modified January 26 01:48 EST 2020. Contains 331270 sequences. (Running on oeis4.)